Multiple choice

A coin is tossed 6 times. The probability of getting a head three times is

  1. 1/2

  2. 3/64

  3. 1/8

  4. 5/16
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D Correct answer
Explanation

This is a binomial probability problem: n=6, k=3, p=0.5. P(X=3) = 6C3 * (0.5)^3 * (0.5)^3 = 20 * (1/64) = 20/64 = 5/16.

AI explanation

Using the binomial probability formula, the probability of getting exactly k successes in n independent trials is the combination of n taken k at a time multiplied by the probability of success to the power of k multiplied by the probability of failure to the power of (n minus k). For a coin tossed 6 times with a success probability of 1/2, the calculation is the combination of 6 taken 3 at a time multiplied by (1/2) cubed multiplied by (1/2) cubed. This evaluates to 20 times 1/8 times 1/8, giving a final probability of 5/16.

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